The useful analytic houses of Weyl transforms as bounded linear operators on $ L^{2}({\Bbb R}^{n}) $ are studied when it comes to the symbols of the transforms. The boundedness, the compactness, the spectrum and the sensible calculus of the Weyl remodel are proved intimately. New effects and strategies at the boundedness and compactness of the Weyl transforms by way of the symbols in $ L^{r}({\Bbb R}^{2n}) $ and by way of the Wigner transforms of Hermite capabilities are given.

This quantity incorporates a number of refereed papers awarded in honour of A. M. Macbeath, one of many major researchers within the region of discrete teams. the topic has been of a lot present curiosity of past due because it contains the interplay of a couple of diversified issues comparable to staff idea, hyperbolic geometry, and complicated research.

The interplay among differential geometry and partial differential equations has been studied because the final century. This dating relies at the proven fact that lots of the neighborhood homes of manifolds are expressed by way of partial differential equations. The correspondence among sure sessions of manifolds and the linked differential equations could be valuable in methods.